1. Field of the Invention
The invention relates to a method for determining a contour in a space image parameter values, in which a plurality of initial vertices located on a seed contour are defined, said vertices being connected by edges to neighbouring vertices, an energy function having an internal portion which is a function of the curvature at each of the vertices and an external portion determined by the density variation at the location of each of said vertices evaluated, and a final contour is determined by varying the position of the vertices till the energy function reaches a minimum.
2. Description of the Related Art
Such a method can, for example, be used in a medical imaging environment for (semi-)automatically defining the outline of a region of interest or of an object, such as an organ or a tumour, in a 2 or 3 dimensional image. Images of clinical importance can be obtained by a variety of medical imaging modalities for example, a conventional X-ray technique, a CT-scanner, magnetic resonance imaging, single photon emission computerised tomography, positron emission tomography or by means of ultrasound echography. Other areas in which deformable contours can be used are, for example, computer graphics and animation. The defined outline of the object can, for example, be used as a basis for providing quantitative information to a physician, for surface extraction for visualisation or for volume definition.
These imaging technologies generate a discrete three-dimensional scalar volume field where each value is a measure of some physical property, for example density. One way of analyzing and displaying the raw scalar field is to generate a geometric model of the scanned object using the volume data as a measure of the object configuration. One approach is to create a "seed" model in the volume data set and then deform the model by a relaxation process that minimizes a set of constraints that are associated with each vertex in the model. The constraints control local deformation, interaction between the model and the data set, and the shape and topology of the model. By minimizing these constraints, one achieves an effect similar to inflating a balloon within a container or collapsing a piece of shrink wrap around an object.
Such a geometrically deformed model is created by specifying first the behavior and characteristics of the model being defined, then selecting constraints to achieve the desired behavior, and finally developing functions that model the constraints. Orthogonal behaviors must be specified. A first one is a mechanism for generating gross deformations. In the balloon analogy, this mechanism expands the balloon. A second mechanism is needed that will interact with the data set and identify voxels on the desired object boundary. This function restricts the balloon from expanding through the boundary of the object being modelled.
Each of these behaviors can be modelled by a term in a local cost function associated with each vertex in the model. These cost functions are also referred to as potential functions. In the following detailed description such potential functions are also collectively referred to as an energy function. The first mechanism is hereinafter referred to as the internal portion of this energy function and the second mechanism is hereinafter referred to as the external portion of this energy function.
The term energy function is not related to physical energy, but is used because the procedure of contour definition has some resemblance to a string of interconnected masses moving in a field of varying potential energy and trying to establish a stable situation of minimum energy. In this similarity the external portion of the energy function corresponds to the density or potential energy and the internal portion to the mutual interaction of the elements of the string.
Such a method for defining is known from an article by J. V. Miller et al., entitled "Geometrically deformed models: A method for extracting closed geometric models from volume dam", published in Computer Graphics, Vol. 25, No. 4, (1991), pages 217-226. In that article a contour is described as a set of vertices connected by edges. The energy function comprises a topology preserving energy term, dependent on an estimation of local curvature and the distance between a vertex and its neighbours, an image event energy term, derived from the density (or pixel values), and a locally defined deformation potential driving the vertices outward or inward. The energy function is evaluated for the vertex positions, not for the trajectory of the connecting edges. This makes the contour discrete, whereby the resolution is determined by the length of the edges. Processing of a seed contour, entered by an operator as a number of vertex points, to a final contour occurs in an iterative procedure. During each step the vertices are moved in the direction of steepest descent along the surface provided by the energy function. Movement of a vertex stops when no energy reduction occurs.
In the known method, the value of the energy function can decrease if a vertex is displaced along an edge and, therefore, the different vertices tend to cluster in corners of the contour. Another disadvantage is that the contour may collapse or expand within a region in which no density variation is present. To avoid such behaviour the known method needs the topology preserving term in the energy function. This topology maintaining term provides constraints or interactions between vertices which are artificial and not related to the density variation in the space. Accordingly, deviations between the contour obtained and the actual shape of the object may occur due to these constraints.